Question

The graph of f(t)=7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?

A. Every year, the coin is worth 7 more dollars

B. When it was purchased (year 0), the coin was worth $7

C. In year 1, the coin was worth 14$

D. When it was purchased (year 0), the coin was worth $2

Answer 1

Option B

When it was purchased (year 0) the coin was worth $7

Explanation:

we have

`f(t)=7(2)^(t)`

This is a exponential function of the form

`y=a(b)^(x)`

where

a is the initial value

b is the base

In this problem we have

a=$7

b=2

b=1+r

so

2=1+r

r=1

r=100%

The y-intercept is the value of the function when the value of x is equal to zero

In this problem

The y-intercept is the value of a rare coin when the year t is equal to zero

`f(0)=7(2)^(0)`

`f(0)=\$7`

therefore

The meaning of y-intercept is

When it was purchased (year 0) the coin was worth $7